Question: $2ij - 2ik - 10i + 1 = -4j + 7$ Solve for $i$.
Solution: Combine constant terms on the right. $2ij - 2ik - 10i + {1} = -4j + {7}$ $2ij - 2ik - 10i = -4j + {6}$ Notice that all the terms on the left-hand side of the equation have $i$ in them. $2{i}j - 2{i}k - 10{i} = -4j + 6$ Factor out the $i$ ${i} \cdot \left( 2j - 2k - 10 \right) = -4j + 6$ Isolate the $i$ $i \cdot \left( {2j - 2k - 10} \right) = -4j + 6$ $i = \dfrac{ -4j + 6 }{ {2j - 2k - 10} }$ We can simplify this by multiplying the top and bottom by $-1$. $i= \dfrac{4j - 6}{-2j + 2k + 10}$